Anal. Chem. 2004, 76, 31-39
Integrated Microanalytical System Coupling Permeation Liquid Membrane and Voltammetry for Trace Metal Speciation. Theory and Applications P. Salau 1 n and J. Buffle*
Chimie Analytique et Biophysicochimie de l’Environnement (CABE), Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211 Geneva 4, Switzerland
We recently described a mini permeation liquid membrane (miniPLM) cell that allows one to record in real time the complete time evolution of the metal strip concentration during an accumulation experiment, where metals are transported uphill from the sample (source) solution to the strip solution through a thin flat sheet PLM. To correlate our results with a theoretical basis and to further improve this miniPLM cell, we present here a simplified model based on diffusion-limited transport under steadystate conditions. This model takes into account the cell geometry (depth of the strip channel), diffusional parameters of metal species in both source and strip solutions, and the equilibrium constants of metal complexes in the source and strip solutions. Also included in the model are the inert and labile complexes formed by the metal in the source solution with hydrophilic ligands. Analytical expressions have been derived by assuming steady-state conditions. Theoretical calculations show the influence of the source diffusion layer thickness, of the strip channel depth, and of the complexation strength of the strip ligand on both the equilibration time and fluxes. The model predicts that, under conditions where the equilibrium in the source solution is little perturbed, the concentration in the strip solution at the end of the accumulation is directly proportional to the concentration of the free metal ion in the source solution, irrespective of the nature of the hydrophilic complexes. If the transport through the source solution is the limiting step, the concentration of labile complexes can be calculated from the initial flux. The results were found to accurately describe the experimental results obtained with the miniPLM cell for Pb and Cd in noncomplexing media. The distribution coefficient KD for Cd was found to be 13, and under optimal conditions, the source diffusion layer thickness δso was estimated to be 9.2 ( 0.7 µm. The technique of permeation liquid membrane (PLM) is a powerful tool for the analysis and speciation of trace metals. There has been growing interest in this field during the past few years.1-10 The PLM technique (Figures 1 and 2) consists of two aqueous solutions, the test (or source) solution and the strip * Corresponding author: (fax) +41.22.702.60.69; (e-mail) Jacques.Buffle@ cabe.unige.ch. 10.1021/ac034264q CCC: $27.50 Published on Web 11/22/2003
© 2004 American Chemical Society
Figure 1. Schematic representation of the miniPLM cell. Crosssectional view. . indicates that the source solution flow is perpendicular to the plane of the sheet. WE, working electrode; AE, auxiliary electrode. hst ) 480 ( 20 µm.
solution, respectively, separated by a thin membrane impregnated with an organic solvent containing a selective carrier, C, for the metal of interest M. M is complexed by C at the sourcemembrane interface, and the complex MC diffuses to the membrane-strip interface where M is released by complexation with a strong ligand S present in the strip solution. Passive transport is achieved and high accumulation factor F, defined as (1) Salau ¨ n, P.; Berdondini, L.; Bujard, F.; Koudelka-Hep, M.; Buffle, J. Electroanalysis, in press. (2) Buffle, J.; Parthasarathy, N.; Djane, N. K.; Matthiasson, L. In IUPAC Series on Analytical and Physical Chemistry of Environmental Systems, 2000; Vol. 6, pp 407-493. (3) Parthasarathy, N.; Salau ¨ n, P.; Pelletier, M.; Buffle, J. ACS Symp. Ser. 2002, No. 811, 102-124. (4) Parthasarathy, N.; Pelletier, M.; Buffle, J. Anal. Chim. Acta 1997, 350, 183195. (5) Parthasarathy, N.; Buffle, J. Anal. Chim. Acta 1993, 284, 649-59. (6) Parthasarathy, N.; Buffle, J.; Gassama, N.; Cuenod, F. Chem. Anal. (Warsaw) 1999, 44, 455-470. (7) Papantoni, M.; Djane, N. K.; Ndungu, K.; Jonsson, J. A.; Mathiasson, L. Analyst 1995, 120, 1471. (8) Djane, N. K.; Ndungu, K.; Malcus, F.; Johansson, G.; Mathiasson, L. Fresenius J. Anal. Chem. 1997, 358, 822. (9) Djane, N. K.; Bergdahl, I. A.; Ndung’u, K.; Schu ¨ tz, A.; Mathiasson, L. Analyst 1998, 123, 393. (10) Sastre, A. M.; Madi, A.; Alguacil, F. J. J. Membr. Sci. 2000, 166, 213-219.
Analytical Chemistry, Vol. 76, No. 1, January 1, 2004 31
Figure 2. Schematic representation of concentration gradients for the transport of M through the PLM in the presence of inert (A) and labile complexes (B) just after the time lag (I) and at equilibrium (II). Schemes in (A II) and (B II) are based on the assumption that (M)bso and Cbso are the same for inert and labile complexes.
the ratio of metal concentration in the strip and in the source solution, can be obtained.4 This transport will proceed until the equilibrium is reached, i.e., when the chemical potential of the free metal ion M in the strip solution equals that of the source solution (Figure 2A II and B II). The overall flux J through the system is thus time dependent. However, since analytical applications of the PLM systems are often set up in such a way as to keep the activity of the metal ion in the strip solution (complete trapping) very low, the equilibrium state is not reached during the measurement time if the source metal concentration is kept 32 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
constant. The corresponding models applied to predict the overall flux do not take into account the time evolution of the concentration in the strip solution and focus only on the initial flux J0.2,11 Depending on the chemical and hydrodynamical conditions, J0 can be limited by the transport through the PLM,11 by the interfacial chemical reactions,12,13 or by the transport in the source (11) Danesi, P. R. Sep. Sci. Technol. 1984-85, 19, 857-894. (12) Danesi, P. R.; Horwitz, E. P.; Vandegrift, G. F.; Chiariizia, R. Sep. Sci. Technol. 1981, 16, 201-211. (13) Fyles, T. M. J. Membr. Sci. 1985, 24, 229-243.
Figure 3. Comparison of the normalized theoretical evolution of the accumulation factor with time for an inert complex and a labile complex for different values of Rso. The arrow indicates the increase of Rso: 1, 2, 5, 20, and 50. The curve corresponding to Rso ) 1 applies for noncomplexing media or for inert complexes. Inset: Comparison of the theoretical time evolution of the accumulation factor in the presence of labile complexes -5 cm2‚s-1, l ) for different values of Rso. Values of the other parameters are realistic values for our PLM system: δso ) 15 µm, DM so ) Dst ) 10 MC -8 2 -1 25 µm, Dm ) 5 × 10 cm ‚s , KD ) KP[C] ) 1200, and Rst ) 400.
solution.10,14 This last case is important for application of PLM in metal speciation analysis in complex media such as environmental ones. In principle,2 under conditions where the depletion of M in the source solution is negligible, two important pieces of information can be obtained by recording the time evolution of the accumulation factor F: (a) [M]bso () free metal ion concentration in the bulk source solution) can be obtained from the equilibrium value, Fe, of F(t) at t ) ∞; (b) Cbso () total concentration of labile metal complexes in the bulk source solution) can be obtained from the initial flux J0 when the permeability of the source solution is the slowest step, whereas [M]bso is obtained from J0 when the permeability of the membrane is the rate-limiting step. Labile complexes are defined as those that can dissociate and form many times during their transport by diffusion through the source diffusion layer. These complexes, as well as free M, play a key role in biouptake by microorganisms in the environment. Both [M]bso and Cbso are thus important parameters to determine in natural waters. PLM is a promising technique for this purpose. By recording the full F(t) curve, these two parameters can be determined. However, with classical systems,15 this record is a long procedure since each data point may take from a few minutes to an hour to be obtained. Recently, we developed a specific PLM minicell based on microtechnology (Figures 1 and 5; ref 1), which enables us to record the F(t) curve in real time in one run. The purpose of the present paper is to describe results obtained with this minicell and to provide a general theoretical support for the interpretation of these F(t) curves. The theory provides F(t), in the absence and presence of ligands forming inert and labile complexes, as function of hydrodynamic conditions in the source solution and of membrane and strip solution parameters. The experimental results support the last two types of aspects of the
theory. Systematic studies of inert and labile complexes are published elsewhere.16,17 THEORY The sensing device used in the miniPLM cell is shown in Figure 1. More details are given in the following Experimental Section and in ref 1. During the accumulation, the source solution is flowing at a given flow rate φ. Metals are transported through the PLM into the stagnant strip solution where they get accumulated. The detection is performed in the strip solution in real time by doing successive voltammetric measurements at a microfabricated Ir-based Hg-plated microelectrode array (WE), placed at the bottom of the strip solution. Therefore, the strip ligand must form complexes that are either electroactive themselves or sufficiently labile to be detected at microelectrodes while being sufficiently strong to keep a low free metal concentration in the strip in order to get a high accumulation factor. These conditions limit the choice of possible ligands, in particular the lability criteria at microelectrodes, which is more restrictive than at macroelectrodes. From the resulting voltammograms, the F(t) curves are deduced. The thickness of the strip channel hst is made small (hst ) 480 ( 20 µm) in order to get a small effective strip volume Vst and a quick response time of the system. Theoretical Background. The model has been developed for a source solution containing either inert complexes MI or labile complexes ML, where I and L are hydrophilic ligands. Figure 2 (14) Guyon, F.; Parthasarathy, N.; Buffle, J. Anal. Chem. 1999, 71, 819-826. (15) Parthasarathy, N.; Pelletier, M.; Tercier-Waeber, M.-L.; Buffle, J. Electroanalysis 2001, 13, 1305-1314. (16) Tomaszewski, L.; Buffle, J.; Galceran, J. Anal. Chem. 2003, 75, 893-900. (17) Zang, Z.; Buffle, J.; Van Leeuwen, H., in preparation.
Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
33
schematically shows the concentration gradients of the various species of M in the source, strip solutions, and membrane, in the presence of inert (A) and labile (B) complexes, during the initial flux (I) and at equilibrium (II). In the former case, the complex MI is in equilibrium with M and I in the bulk solution, but its dissociation rate constant is so low that it has no time to dissociate during its residence time in the source diffusion layer δso. Thus, it does not contribute to the flux (Figure 2A I). Conversely, labile complexes ML have dissociation rate constants large enough to be always at equilibrium with M and L in the source diffusion layer (Figure 2B I), and both M and ML contribute to the overall flux. In both cases A and B, the free metal ion concentration in the strip solution [M]bst will increase until the chemical potential in the strip is equal to that in the source solution, i.e., [M]bst ) [M]bso. Thus, accumulation factor at equilibrium, Fe, cannot discriminate between inert and labile complexes (Figure 2A II and 2B II). To derive the complete F(t) curves, the following assumptions are made based on both experimental (in particular, geometric condition of the cell presented in Figure 1) and theoretical grounds: (a) Only linear concentration gradients are considered inside the membrane, as depicted in Figure 2A I and 2B I. Consequently, the resulting equations are applicable only after establishment of an initial time lag tlag. (b) The complexes ML or MI do not diffuse through the PLM and thus do not contribute to the overall flux. (c) The condition VstRst < < VsoRso applies. This condition implies2 that Cbso and [M]bso are not depleted due to the transport through the membrane and, thus, that Rso remains constant all along the measurement. This is typically the case for measurements with a microliter cell dipped in a lake or river. (d) Both source and strip diffusion layer thickness (δso and δst, respectively) are constant during the PLM accumulation step and homogeneous over the whole surface area A of the PLM. δso is controlled by hydrodynamic conditions at the source-PLM interface. δst is fixed by molecular diffusion and strip channel geometry (see Diffusion Layer Thickness inside the Strip Solution). (e) The interfacial complexation reactions of M and C on both source and strip sides are fast and not rate limiting,14 and the distribution coefficient KD of M between the aqueous (either source or strip) solution and the organic phase is assumed to be identical on both source and strip sides:
KD )
[MC]im [M]iso
)
[MC]jm [M]jst
) KM p [C]
(1)
whereKM p is the partition coefficient, [C] is the carrier concentration in the PLM, [M]iso and [M]jst are the free metal ion concentrations in the aqueous phase at the source-membrane and strip-membrane interfaces, respectively, [MC]im and [MC]jm are the corresponding concentrations of the complex MC, in the PLM. (f) The strip ligand S is in large excess compared to the metal accumulated at equilibrium in the strip solution, i.e., Rst remains constant during the accumulation step. (g) The strip solution volume is Vst ) Ahst, hst being the depth of the strip compartment (Figures 1 and 2). Diffusion Layer Thickness inside the Strip Solution. The concentration profile at time t in the strip compartment is fixed 34
Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
on one side by the flux, Jst, released from the PLM at x ) 0 [Jst ) DM st (∂Cst/∂x)x)0] and on the other side by the fact that the wall surface at x ) hst, opposite to the PLM, is an impermeable surface M [DM st (∂Cst/∂x)x)hst ) 0] (Figure 2). Dst is the average diffusion coefficient of M and MS in the strip compartment. For such a case, when Cst ) 0 at t ) 0 for 0 e x e hst, the time evolution of the concentration profile Cst ) f(x) for a constant incoming flux Jst, is given by eq 2:18 with 0 e x e hst.
Cst )
[
Jsthst DM st t DM st
hst
2
+
3(hst - x)2 - hst
2
∞
∑
6hst (-1)n
π2n)1 n2
exp
2
-
2
( ) 2 2 - DM st n π t
hst
2
]
nπ(hst - x)
cos
hst
(2)
A concentration profile independent of time occurs after a certain time, tlag, corresponding to the diffusion time in the strip solution (∼100-200 s for 480 µm). For t > tlag, the third term into the brackets of eq 2 tends to zero and the thickness of the diffusion layer in the strip solution, δst, can then be computed by eq 3, whereCist is the strip concentration of total M at the mem-
δst )
Cist - Cbst M Dst Jst
(3)
brane-strip interface (x ) 0) and Cbst is the strip concentration of total M at x ) hst. Combining eqs 2 and 3 for t > tlag, we get
δst ) hst/2
(4)
In our case, Jst does not remain constant during the accumulation period, but slowly decreases until it reaches a zero value corresponding to the equilibrium state. However, the change of Jst with time is much slower (thousands of seconds) than the diffusion time in the strip solution so that the concentration profile given by eq 2 is a good approximation all along the accumulation period after t ) tlag. Curves Cbst(t) ) f(t) in the Absence of Complexes and for Inert Complexes. With the assumptions made in section Theoretical Background, the fluxes through the source solution, Jso, the membrane, Jm, and the strip solution, Jst, are given by eqs 5-7:
DM so Jso ) ([M]bso - [M]iso) δso Jm )
(5)
DMC m ([MC]im - [MC]jm) l
(6)
Dst i (C - Cbst) δst st
(7)
Jst )
(18) Crank, J. The mathematics of diffusion, 2nd ed.; Oxford University Press Inc.: New York, 1975; p 61.
Rso - 1 M 1 DM + DML so ) Dso so Rso Rso
Equation 5 takes into account only the free metal ion concentration [M]bso since MI is not dissociated. In the strip solution, one gets
Cbst ) [MS]bst + [M]bst
(8) Combining eq 13 with eqs 4, 6, 7, and 10 again leads to eq 11 for F(t) but with
and
DM st
)
Rst - 1 1 + DMS st Rst Rst
DM st
(9)
with Rst ) Cbst/[M]bst. The overall flux, J(t), is given by
J(t) )
Vst ∂Cst ∂Cst ) hst A ∂t ∂t
(10)
where Cst is the average total metal concentration in the strip solution. At steady state, J(t) ) Jso ) Jm ) Jst. By integrating eq 2 for t > tlag, it can be shown that Cst ) Cbst + Jsthst2/DM st . The second term becomes negligible at long time. Above all, since Jst decreases very slowly in comparison with the diffusion time in the strip solution, the time evolution of the second term is very small and we can approximate ∂C h st/∂t ) ∂Cbst/∂t. Combining eqs 5-7 and 10 and this approximation, we get
F(t) )
Cbst Cbso
)
[
)]
(
- k(t - tlag) Rst 1 - exp Rso Rsthst
(11)
with
k)
(
δso
l
Dso
DMC m KD
+ M
+
hst 2DstMRst
)
-1
(12)
Since the sole species responsible for the flux is the free M, eq 11 also applies to noncomplexing media (Rso ) 1). Labile Complexes. In the presence of labile complexes, the equilibrium exists between M and L even within the source diffusion layer; i.e., Ciso ) [M]isoRso, where Ciso is the total concentration of M at the source side of interface i. Equation 5 should then be replaced by eq 13 since complexes are dissociating in the source diffusion layer and thus contribute to the diffusion flux in the source solution. In that case
DM so Jso ) (Cb - Rso[M]iso) δso so
(13)
Cbso ) [ML]iso + [M]bso
(14)
where
and
(15)
k)
(
δso
DM soRso
+
l DMC m KD
hst
+
2DM st Rst
)
-1
(16)
i.e., Rso is now included in k. F(t) Curves, Initial Fluxes, and Equilibration Times. Figure 3 shows curves for F(t) for inert and labile complexes, with the same value of parameters (eq 11). It shows that when t f ∞, F(t) f Rst/Rso for both labile and inert complexes, which enables one to determine [M]bso, irrespective of the degree of lability of the corresponding complexes. In the case of inert complexes, the time te needed to reach equilibrium is independent of the degree of complexation Rso. Conversely, the increase of F(t) is largely influenced by the dissociation of the labile complexes that increases the initial flux. te is thus significantly shorter than in the presence of inert complexes. (1) Equilibration Time. Strictly speaking, equilibrium is reached at t ) ∞. In practice, however, it is useful to compute teas the time required to reach 90 or 95% of equilibrium. Using F(te)/F(∞) ) 0.9, we get from eq 11
te - tlag ) 2.3Rsthst/k
(17)
where k is given by eq 12 in the absence of complexes or in the presence of inert complexes and by eq 16 for labile complexes. The time for equilibration is thus strongly dependent on hst and Rst in both cases and is also largely influenced by Rso (which is included in k) in the case of labile complexes. To get short equilibration time in the presence of inert complexes or in noncomplexing media, the depth of the strip compartment should be as small as possible and the use of not too strong ligand (Rst not too large) in the strip solution is recommended while keeping Rst > Rso. However, the exact roles of Rso and Rst strongly depend on the relative importance of the three terms in eqs 12 and 16. (2) Initial Flux, J0. The initial flux J0 is computed by combining and rearranging eqs 10 and 11
J0 ) kCbso(Rso)-1
(18)
where k is again given by eq 12 in the absence of complexes and for inert complexes and by eq 16 for labile complexes. The main difference in J0 for inert and labile complexes arises from the parameter Rso present in the first term of the k parameter, for labile complexes. In most cases, the third term in parentheses in eqs 12 and 16, which corresponds to the inverse of the diffusion flux in the strip solution, is negligibly small with respect to the other two terms, in particular in microsystems (hst small) and in strongly complexing strip solution (Rst large). Then, either Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
35
diffusion fluxes in the source solution or in the membrane (or both) are the limiting factors for the initial flux. The so-called permeability criterion, π, is based on the relative importance of these two terms in eq 12 or 16. It indicates whether the limiting flux is the diffusion flux in the source solution (π . 1) or in the membrane (π , 1). In the absence of complexes and for inert complexes, we get M π ) δsoKDDMC m /lDso
(19)
while for labile complexes, we get M π ) δsoKDDMC m /lDsoRso
(20)
Three extreme values of the initial fluxes (eq 18) apply in the following limiting cases. The validity of these equations have been checked experimentally:16,17 (a) If π < < 1, the initial flux for both labile and inert complexes becomes b J0 ) (KDDMC m /l)[M]so
(21)
J0 is then directly proportional to the free metal ion concentration, like Fe, irrespective of the lability of complexes, because the flux through the membrane is not sufficient to create a concentration gradient at the source-membrane interface. (b) If π > > 1, and complexes are inert, eq 18 becomes b J0 ) (DM so/δso)[M]so
(22)
J0 is still proportional to [M]bso but with a different proportionality constant, because the noncontribution of complexes is due to their too slow dissociation rate, rather than to the low flux through the system. Correct interpretation of the initial flux must then be based on a clear analysis of the nature of the limiting step in the flux. (c) If π > > 1, and complexes are labile, eq 18 becomes
J0 )
DM so b C δso so
(23)
J0 is now directly proportional to the total concentration of labile complexes, because the consumption of M at the sourcemembrane interface is strong enough to create a concentration gradient of M in the source diffusion layer, which in turn results in dissociation of ML. (3) Effect of Cell Geometry and Hydrodynamic Conditions on F(t). The depth of the strip channel hst has a strong influence on F(t) (Figure 4A) and thus on the equilibration time due to the fact that the number of moles required to reach equilibrium in the strip solution increases with hst. hst should then be as small and reproducible as possible. Cells produced by microtechnology are thus required. The effect of the source diffusion layer thickness, δso has been studied in the range 10-100 µm. Two sets of values are presented: π ) 4.8 (Figure 4B) and π ) 0.04 (Figure 4C). The 36
Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
Figure 4. Time evolution of accumulation factor F. (A) effect of hst; (B, C) effect of δso.(A) δso ) 20 µm. (B) hst ) 480 µm, KD ) 1200 (π ) 4.8). (C) hst ) 480 µm, KD ) 10 (π ) 0.04). Other values: DM so ) -8 cm2‚s-1, R Dst ) 10-5 cm2‚s-1, l ) 25 µm, DMC so ) 1, m ) 5 × 10 and Rst ) 200.
parameters used are typical values for Pb and Cd, respectively. A large dependence of F(t) on δso is observed for π > 1, which implies that the stirring rate or the flow rate of the source solution should be well controlled. Conversely, when the limiting flux is the flux through the PLM, i.e., π < 1 (Figure 4C), the influence of δso is negligible since there is almost no concentration gradient in the source solution.
All reagents used were of Pro. Anal. reagent grade, and all solutions were freshly prepared with Milli-Q water. The strip solution is 10-2 M sodium pyrophosphate (Merck) adjusted to pH 6,0 with Suprapur HNO3 (Baker). Source solutions was 10-2 M morpholinoethanesulfonic acid (MES) adjusted to pH 6,0 with Suprapur LiOH (Fluka). This buffer solution does not complex either Pb or Cd.19 All the experiments were carried out at room temperature. The electrochemical measurements were performed using a computer-controlled Ecochemie µ-Autolab potentiostat (Utrecht, The Netherlands), and data were treated using the associated GPES software (version 4.8). The source solution was made flowing by means of a peristaltic pump (Minipulse, Gilson).
Figure 5. Schematic representation of the assembly of miniPLM cell. Exploded view.
EXPERIMENTAL SECTION Accumulation and detection of metals have been done in noncomplexing media using the microanalytical system described in detail in ref 1 and shown in Figures1 and 5. The miniPLM cell is made of different parts: the working electrode (WE) is a microfabricated square array of 3 × 5 Ir-based Hg-plated microelectrodes. The Ir auxiliary electrode (AE) is placed closed to the WE and is also of microsize (0.25 mm2). Both electrodes are surrounded by a containment ring made of UV patterned Epon SU-8 of 280 ( 20 µm thickness, which is filled with an adsorbing gel (1.5% LGL agarose + 10% C18 particles) to prevent adsorption of the organic solvent leached from the PLM onto the Hg surface. Epon SU-8 structures are also used to form part of the strip channel. The reference electrode is a homemade miniaturized Ag/ AgCl/KCl (3 M)//NaNO3 (0.1 M). The flat sheet PLM is a polypropylene Celgard 2500 having a thickness of 25 µm, and the strip and source spacers are Teflon pieces of 200-µm thickness. After impregnation of the PLM with the organic solution (equimolar mixture (0.1 M) of didecyl-1,10-diaza-18-crown-6 ether (22DD) and lauric acid in phenylhexane/toluene (1:1 v/v) solution), the system is mounted by stacking and pressing these different parts as depicted in Figure 5. During the accumulation, the source solution is flowing and metals are accumulated in the stagnant strip solution (10-2 M Na4P2O7, pH 6.0). This pyrophosphate ligand forms labile complexes with Cu, Pb, and Cd.1,15 The evolution of Cbst is then followed in real time in the strip solution using square wave anodic stripping voltammetry (SWASV). The SWASV peak intensities were used to calculate the accumulation factor as explained in ref 1. Accumulations of known concentrations of Pb and Cd have been studied for different hydrodynamic conditions at the sourcemembrane interface. These have been modified either by changing the source flow rate or by changing the opening size of the source spacer. Two different sizes have been used: s/w ) 0.29 and s/w ) 0.131, where s is the thickness of the Teflon spacer and w the width of the window (Figure 5).
RESULTS AND DISCUSSION Accumulation Curves F(t). The complete accumulation curves of Pb and Cd have been recorded from a source solution containing respectively 10 and 100 nM of these two metals. Figure 6 (open symbols) shows the experimental curve F(t) for Pb and Cd together with the fitting curve obtained from eq 11. The only fitted value for Pb is the thickness of the diffusion layer δso. All -6 cm2‚s-1,20 R others parameters were known: DM so so ) 9.5 × 10 MC 21 ) 1, l ) 25 µm, KD ) 832 ( 64, Dm ) (5 ( 1) × 10-8 cm2‚s-1,21 -6 cm2‚s-1.1 The time lag is hst ) 480 µm, and DM st ) 4.8 × 10 directly determined from the experimental F(t) curve and is tlag ) 90 s, in complete agreement with the value found with numerical simulation.22 For the pyrophosphate solution, the following values of the complexation constants have been used 23 for Pb log β1 ) 7.18 and log β2 ) 10.03, and for the acid-base constants:24 log H H H βH 1 ) 8.3, log β2 ) 14.3, log β3 ) 17.0, and log β4 ) 19.5. They correspond to the ionic strength employed in this work. Using these values, Rst is equal to 385. Best fitting was then obtained using δso ) 9.2 ( 0.7 µm. To fit the experimental data of Cd, we assumed that DCdC ) m PbC Dm , which is probably a valid assumption since same diffusion coefficients were previously found for PbC and CuC in the PLM membrane ((5 ( 1) × 10-8 cm2‚s-1 21 and (5.2 ( 0.5) × 10-8 cm2‚s-1,14 respectively), and δso ) 9.2 ( 0.7 µm, i.e., the same source diffusion layer thickness as the one determined for Pb. -6 Using these two values and the following ones, DM so ) 7.2 × 10 -6 cm2‚s-1,20 Rso ) 1, l ) 25 µm, hst ) 480 µm, DM st ) 4.2 × 10 2 -1 1 cm ‚s , and tlag ) 90 s, the best fitting was obtained using KD ) 13 and Rst ) 8.7. The value of KD is in agreement with that previously found17 (∼13) with the same PLM system. In addition, its low value is in agreement with the lower transport of Cd through the PLM observed experimentally compared to Cu and Pb.5 From Rst ) 8.7, it is found that log β(Cd-P2O7) ) 5.54, which is however lower than the reported values (6.03-8.7 23), but of similar order of magnitude considering the wide spread of these values and the limited available data.
(19) Soares, H. M. V. M.; Conde, P. C. F. L.; Almeida, A. A. N.; Vasconcelos, M. T. S. D. Anal. Chim. Acta 1999, 394, 325. (20) Heyrovsky´, J.; Kuta, J. Principles of polarography; Czechoslovak Academy of Sciences: Prague, 1965. (21) Slaveykova, V.; Buffle, J. Sci. Total Environ., in press. (22) Salau ¨ n, P.; Josserand, J.; Morandini, J.; Girault, H. H.; Buffle, J. J. Electroanl. Chem., in press. (23) Martell, A. E.; Smith, R. M. Nist standard reference database 46, Version 5.0, 1998. (24) Sille´n, L. G.; Martell, A. E. In Special publication 25, Chemical Society: London, 1964.
Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
37
Figure 6. F(t) accumulation curves for Pb and Cd. Open symbols: experimental data points for s/w ) 0.13 (φ ) 8.3 mL/min). Black symbols: experimental data points for s/w ) 0.29 (φ ) 9.8 mL/min). Full line: eqs 11 and 12. Experimental conditions: source solution, MES (10-2 M), pH 6.00, [Pb] ) 10 nM, [Cd] ) 100 nM. Strip solution: Na4P2O7 (10-2 M), pH 6.00. Voltammetric conditions: preclean at 0 V for 15 s, deposition at -1.25 V for 30 s, potential scan from -1.25 to 0 V, frequency 50 Hz, SWASV amplitude 25 mV, and step amplitude 9 mV. Measurement were done every ∼3 mn. Parameters for theoretical fitting, see text.
Figure 7. Time evolution of the SWASV peak height Pb and Cd during the PLM accumulation at different source linear speed. Strip solution: Na4P2O7 (10-2 M), pH 6.00. Source solution: MES (10-2 M), [Pb] ) 10 nM, [Cd] ) 100 nM, pH 6.00, s/w ) 0.29. SWASV measurement conditions: conditioning at 0 V for 50 s, deposition at -1.25 V for 60 s, stripping from -1.25 to 0 V, frequency 50 Hz, SWASV amplitude 25 mV, and step 9 mV. Measurement were done every ∼2 mn.
From the fitted parameters, the permeability criteria can be evaluated for both metals using eq 19. Under these conditions, π ) 1.6 and 3.1 × 10-2 for Pb and Cd, respectively. Thus, the transport should then be limited by the permeability through the membrane for Cd, while in the case of Pb, the overall transport should be influenced by the thickness of the source diffusion layer. Evidence of this is given below. Influence of the Source Flow Rate on the Initial Fluxes. The first evidence is shown by comparing the curves with open symbols (s/w ) 0.13) and black symbols (s/w ) 0.29) in Figure 6, which were obtained for an almost identical source solution flow rate (8.3 and 9.8 mL/min, respectively). It can be seen that, while the transport of Cd is unaffected by the form ratio s/w, the transport of Pb is strongly dependent on it. This is consistent with the previous observations: when the opening size is larger (s/w ) 0.13), the diffusion layer thickness δso gets thinner, thus increasing the overall transport of metals that are limited by the permeability through the source solution (Pb in our case). However, if the transport is limited by the permeability through the PLM (in the case of Cd), the influence of the s/w ratio is nil. 38 Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
A more detailed study has been done by varying the source solution flow rate φ between 1.22 and 9.86 mL‚mn-1 for s/w ) 0.29. Figure 7 shows the time evolution of the SWASV peak current height for Pb and Cd for each φ tested. In both cases, the increase of peak current height, and thus concentration, is almost linear versus time at high flow rate (φ ) 9.86 mL/min). From Figure 7, F(t) curves have been plotted for each flow rate value and (∂F/∂t)t)tlag has been plotted as a function of φ (Figure 8.). From eqs 11, 12, 16, and 21-23, it can also be shown that in all cases ∂F/∂t ) J0/Cbsohst; i.e., ∂F/∂t is proportional to J0. Thus, Figure 8 shows that, for Pb, the initial flux J0 is strongly influenced by the source linear flow rate, while for Cd, it remains almost constant. This evidence means that, for further application in the presence of hydrophilic complexes, the following must hold: (a) In the case of Cd, both the initial flux J0 and Fe should be proportional to [M]bso, irrespective of the complexing media. (b) In the case of Pb, the initial flux J0 and Fe can allow to determine Cbso and [M]bso, respectively. In this case, a large diffusion layer should be used in order to increase π. If, however, π , 1, only
and S. Pochon for the encapsulation of these electrodes. This work was supported by the MINAST program (1.04- ELCHEM). GLOSSARY
Figure 8. Effect of the source flow rate on the initial flux through the PLM for Pb (square) and Cd (circle). Same conditions as in Figure 7. The error bars have been graphically estimated.
[M]bso can be determined with an indication of the presence or absence of labile complexes from the equilibration time. CONCLUSION Experimental results have been found to be in good agreement with theoretical predictions. Equations F(t) are very useful to set up the right experimental parameters, either chemical or geometrical. For instance, it appears clearly that, to reach the equilibrium state in a reasonable time with a high accumulation factor Fe, the depth of the strip channel should be as low as possible. In our case, hst ) 480 µm; this is probably the maximum depth that should be used. If the interest is now to accumulate as much as possible, this can be done either by changing the concentration of the strip ligand or by changing the pH of the strip solution so that the strip solution acts as a perfect sink. One of the other advantages of the PLM over conventional speciation techniques is its versatility: by changing physical parameters such as the hydrodynamic conditions at the source-membrane interface, the carrier concentration, the nature of the carrier or of the solvent, or both,the π value can be set up to tend either toward a source diffusion-limited transport (π . 1) or toward a membrane diffusion-limited transport (π , 1). In both cases, in the presence of labile complexes, [M]bso can be known from te and quantification of Cbso is possible in the former case. Work in that direction is underway. ACKNOWLEDGMENT We thank AKZO Nobel for giving Celgard membranes as a gift. We also thank F. Bujard for the construction of the miniPLM cell, L. Berdondini for realization of the microfabricated electrode,
R
complexation coefficient
A
surface area
C
total concentration or carrier
D
diffusion coefficient
δ
diffusion layer thickness
F
accumulation factor
hst
depth of the strip compartment
J
diffusion flux
K
complexation constant
KP
partition coefficient
KD
distribution coefficient
l
membrane thickness
M
free metal ion
MC
metal-carrier complex
MI
inert hydrophilic complex
ML
labile hydrophilic complex
MS
metal strip-ligand complex
π
permeability criterion
S
strip ligand
t
time
V
volume
φ
source flow rate
Superscripts b
bulk solution
e
equilibrium
i
source-membrane interface
j
membrane-strip interface
MC
metal carrier complex
0
initial time
Subscripts m
membrane
so
source solution
st
strip solution
t
total
Received for review March 16, 2003. Accepted September 25, 2003. AC034264Q
Analytical Chemistry, Vol. 76, No. 1, January 1, 2004
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